Complex Fds dot proctuduct integral

Unart
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Homework Statement


F(x,y)=<2xy,x^2+y^2>, the path is part of the unit circle in the 1st quadrant. And I'm supposed to calculate ∫F°ds given that info

Homework Equations


My question is if this equation would apply to the following problem
∫F°ds=θ2-θ1
Since this is a circular equation.
 
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Unart said:

Homework Statement


F(x,y)=<2xy,x^2+y^2>, the path is part of the unit circle in the 1st quadrant. And I'm supposed to calculate ∫F°ds given that info

Homework Equations


My question is if this equation would apply to the following problem
∫F°ds=θ2-θ1
Since this is a circular equation.

Not sure where you got that equation, but no, it wouldn't.
 
Ok Thanks!
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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